I'm aware that the rise of Gnosticism was after the New Testament was written - but it would seem that a lot of the ideas on which it was built were floating around at the time. (Particularly Greek ideas about the uncleanness of the body contrasted with the purity of the mind/spirit).

Particularly in 1 Cor 15, but also more generally across the NT - does the Bible contain a rebuttal of the ideas of Gnosticism? (ie that Jesus and subsequent resurrection was physical).

I can't find the source right now, but I recall reading once that a lot of the ideas that eventually coalesced into Gnosticism were originally spread around by Simon (the one from Acts chapter 8) as an act of vengeance/spite after Peter turned him down.
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Mason Wheeler♦Feb 26 '12 at 15:22

2 Answers
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Avoid the irreverent babble and contradictions of what is falsely called “knowledge,”

In doing so, Paul is specifically calling on Timothy not to engage those who claim a special "Gnosis" that somehow elevates them. As such, Paul is not going to take on that heresy himself, but he does still provide the basis for rejecting it.

1 Timothy makes claims that stand in opposition to the docetic beliefs of the Gnostics.

1 Timothy 3:16 makes clear that

He was manifested in the flesh

and goes on to way in 1 Timothy 4

Now the Spirit expressly says that in later times some will depart from the faith by devoting themselves to deceitful spirits and teachings of demons, 2 through the insincerity of liars whose consciences are seared, 3 who forbid marriage and require abstinence from foods that God created to be received with thanksgiving by those who believe and know the truth. 4 For everything created by God is good, and nothing is to be rejected if it is received with thanksgiving, 5 for it is made holy by the word of God and prayer

Gnostics believee that matter itself was evil (and as such could not believe that God would deign to become matter), and as such made anything fleshy out to be bad. Eventually, since everything tangible was bad, they started suggesting that it didn't matter what the flesh did, only the spirit, and so they became libertines, orgiastic, and the like. Paul undercuts the argument he by rejecting the premise.

As Bruce Alderman points out, John may have been reacting to the Gnostic Gospel of Thomas (really just a collection of sayings mores than a narrative as we expect Gospels to be)

It has been debated whether or not Gnosticism predates Christiainity or if in turn Gnosticism grew out of Christianity. In any event, however, the fact that Paul was only mentioning it in his later books (argued by some scholars to actually be written by Pauls followers after his death) shows that much of the NT was already in place before it became a real threat to the church.

John, by contrast, is typically considered to be one of the last books, so a back handed reference fits in perfectly with that assertion.

Later, in 2 John (and here I'll claim same authorship) he writes

For lmany deceivers mhave gone out into the world, nthose who do not confess the coming of Jesus Christ in the flesh. Such a one is the deceiver and the antichrist.

For this perishable body must put on imperishability, and this mortal body must put on immortality.

But throughout the whole passage, Paul is contrasting different types of bodies, not, as the Gnostics did, contrasting an impure physical world and a pure spiritual world.

A couple of the gospels include details that may be intended to rebut an early form of Gnosticism. In Jesus' appearance to the disciples in the upper room in Luke, we see him take a break from teaching and eat a piece of fish:

While in their joy they were disbelieving and still wondering, he said to them, "Have you anything here to eat?" They gave him a piece of broiled fish, and he took it and ate in their presence.

And if the Gnostic "Gospel of Thomas" was written in the first century as some scholars believe, a story from the Gospel of John may be intended as a rebuttal, a way of saying, That's not the Thomas I knew.

But Thomas (who was called the Twin ), one of the twelve, was not with them when Jesus came. So the other disciples told him, "We have seen the Lord." But he said to them, "Unless I see the mark of the nails in his hands, and put my finger in the mark of the nails and my hand in his side, I will not believe." A week later his disciples were again in the house, and Thomas was with them. Although the doors were shut, Jesus came and stood among them and said, "Peace be with you." Then he said to Thomas, "Put your finger here and see my hands. Reach out your hand and put it in my side. Do not doubt but believe." Thomas answered him, "My Lord and my God!"